Extreme Value Theory

Extreme Value Theory

In statistics, any way to estimate or measure the likelihood of an extremely unlikely event. That is, extreme value theory measures the probability that a data point that deviates significantly from the mean will occur. It is useful in insurance to measure the risk of catastrophic events, such as tornados and wildfires.

In addition, Table 3 shows that the best VaR methods for a confidence level of 5% are the GARCH(1, 1), the RiskMetrics[TM] and the dynamic Extreme Value Theory (EVT) methods, in which the percentage of losses exceeding the VaR are very close to the 5% confidence level required.

Considering that a basic assumption from the extreme value theory (TVE) is that the distribution of the maximums of independent and identically distributed random variables, converge to one of the particular cases of the GEV (COLES, 2001), and also based on the assumption that the GEV has all the flexibility of its three particular cases NADARAJAH & CHOI, 2007).

While up to now the Pareto distribution was commonly employed to modeling the tails of loss severities, adjustments with Extreme Value Theory (EVT)-based distributions significantly improve tail distribution inference and analysis.

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